Let A and B be n xn matrices. Which of the following statements are always true?(1) (AB)² = 4²B²(ii) If the homogeneous system Ax = 0 has infinitely many solutions then A is not invertible(iii) If AB = AC then B = C(A) (i) and (ii) only (B) (i) only (C) (ii) and (iii) only (D) (iii) only (E) (i) and (ii) only (F) (ii) only(G) all of them (H) none of them

i AB2=A2B2-Not Trueii Ax=0 has infinity many solution then A is not inversible .…

Answered: Let A and B be nx n matrices. Which of…

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Let A and B be nx n matrices. Which of the following statements are always true? (i) (AB)² = 4²B?

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Matrices

Section2.1: Operations With Matrices

Problem 77E

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Concept explainers

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.

Question

Let A and B be n xn matrices. Which of the following statements are always true?
(1) (AB)² = 4²B²
(ii) If the homogeneous system Ax = 0 has infinitely many solutions then A is not invertible
(iii) If AB = AC then B = C
(A) (i) and (ii) only (B) (i) only (C) (ii) and (iii) only (D) (iii) only (E) (i) and (ii) only (F) (ii) only
(G) all of them (H) none of them

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